A Riemann-Hurwitz Formula for thep-Rank of Ideal Class Groups of CM-Fields

✍ Scribed by Kay Wingberg

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 486 KB
• Volume: 56
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1006/jnth.1996.0021

✦ Synopsis

In this note we prove an analogue of the classical Riemann-Hurwitz formula for the minus part of the p-rank of S-ideal class groups of algebraic CM-fields. The result is an improvement of Kida's formula for the cyclotomic Z p -extension.